The Geometry of Supermanifolds (Mathematics and Its Applications (Kluwer ))

Bartocci, Claudio/ Bruzzo, Ugo/ Hernandez-Ruiperez, Daniel

Kluwer Academic Pub（1992/01発売）

• 製本 Hardcover:ハードカバー版／ページ数 242 p.
• 言語 ENG
• 商品コード 9780792314400
• DDC分類 514.3

Full Description

'Et moi, ...* si favait III mmment en revenir, One service mathematics has rendered the je n'y serais point aile:' human race. It has put CXlUImon sense back Iules Verne where it belongs. on the topmost shelf next to the dUlty canister lahelled 'discarded non- The series i. divergent; therefore we may be able to do something with it. Eric T. Bell O. Hesvi.ide Mathematics is a tool for thOUght. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d't!tre of this series.

Contents

I: Foundations.- I — Elements of graded algebra.- II — Sheaves and cohomology.- II Supermanifolds.- III — Categories of supermanifolds.- IV — Basic geometry of G-supermanifolds.- V — Cohomology of supermanifolds.- VI — Geometry of super vector bundles.- VII — Lie supergroups and principal super fibre bundles.